A Fully Integrated Model for the
Optimal Operation of HydroPower
Generation
by Francois Welt
University of Toronto, Dec. 4, 2012
01/2012
2
Hatch Power and Water Optimization Group
• Engineering Company
• Specialized group within Hatch Renewable Power
• Experience:
– Over 40 systems implemented
– Experience with different types of hydro systems
• Supported by over 9,000 multi-disciplinary
engineering professionals worldwide
01/2012
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3
Hatch Power and Water Optimization
• Water Resource and Power System Modeling –
Simulation and Optimization
• System Implementation
– Configuration, Test
– Integration / Communications
– Install and Train
• Studies
• Asset Management / Life cycle analysis
• Wind Farm Design Optimization
01/2012
3
4
Columbia Vista - Integrated Optimization Model
01/2012
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Hydro Optimization in Generation Planning
Concepts
• Make best use of limited
hydro resources
• Meet operational constraints
• Maximize Profits
– Maximize sales/ Minimize costs
– Calculate optimal plant/unit MW
– Calculate optimal WL trajectory/
spill releases
– Calculate bid curve
Optimization technologies becoming increasingly attractive
with improvements in computing speeds/ capabilities
01/2012
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6
Optimization Statistics
Examples of potential economic benefits from
optimization - Short term operation
Ref: “Assessing the Economic Benefits of
Implementing Hydro Optimization”,
Hydro Review magazine, 1998
1.4
1.2
1
0.8
0.6
Typically, potential
improvements between 1 –
5%
0.4
0.2
0
Market
Spill
Efficiency
Head
01/2012
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7
Hydro Optimization
Time Scale
Plant/
units
Real Time
(RT):
Dispatch
Hour/day
end/
Smaller
reservoir
Short Term
(ST):
• Schedule
• Transactions
To end of
week/month
Larger reservoir
Long Term (LT):
• Generation/Water Plan
• Targets and Water Values
To end of water year
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Optimization Problem
Must formulate problem in terms of:
•Objective functions
•Constraints
•Rules of operation
•Physical relations
•Decision Variables
Objective  Max{ [Re venues( X )  Costs( X )]}
Time
Constra int_ F ( X )  0
Characteristics:
•One set of decisions per time step, piece
of equipment
•Hydraulic network
•Transmission network
•Large problem size
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9
Physical Representation
• Hydraulic Network
–
–
–
–
–
–
Source: Inflow Points
Sink: downstream outlet
Water conveyance/ Flow
Storage
Head (Potential energy) and head loss
Can be bi-directional (gen/pump)
• Electric Network
–
–
–
–
Source: Generation points
Sink: Load or Market points
Bi-directional
Energy losses
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Hydro System Components
River
Reach
10
Inflow Arc
Reservoir Node
Power Arc
Spill Arc
Tailwater Junction Node
River
Reach
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Columbia
River
System
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SCE Vista
Big Creek Hydro System Representation
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Generation
Resource
(Hydraulic flow
to Electric MW)
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Controlled and
Uncontrolled
Spillways
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Rock Island Schematic
Powerhouse Two
Powerhouse One
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
Spillway
F
F
F
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Hydraulic Network Representation
– Continuity equation at each reservoir node
Σ Qin – ΣQout = V(t) – V(t-1)
– Continuity equation at each junction node
Σ Qin – ΣQout = 0
– Conveyance in reach arc
Qout (t) = Σ α(n).Qin(t-n)
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17
Transmission Area
Load Demand
Committed Transactions
X
Market
• Purchase
• Sale
Bilateral
• Purchase
• Sale
D
Transaction
X
H
Hydro Generation
T
Thermal Generation
Wind
Wind
Generation
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“aggregate
unit”
Bus Configuration
COB2P
Contract Bus
BPA1
X(COB2)P
Supply Area River 1
Plant 1
Bus A
COB1
X MW
Y MW
X(COB1)S
X(COB1)P
X(COB2)S
COB2S
Bus B
W MW
X(PNW1)
S
X(PSE) S
X(PNW1)
P
X(PSE) P
COB3S
X(COB3)S
L
X(PNW2)
S
X(PNW2)
P
“line limits”
X(BPA-X) S
BPA3
X(PNW3)
S
X(PNW3)
P
Z MW
X(MIDC)
S
River 2
Plant 4
X(MIDC)P
MID-C
“group line
limits”
Plant 2
Plant 3
BPA2
COB3P
X(COB3)P
PSE
River 3
Plant 5
Plant 6
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LT Vista Physical Model
Transmission System
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Network Representation
• Electric Network
– Continuity equation at node (bus)
Σ MWin – ΣMWout = 0
– Losses through conveyance (tieline)
MWout = Mwin - α.Mwin^2
• MW Energy
• MW ancillary service (reserve)
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21
Physical Representation
Reserves and Generation
• Unit/Plant Balance Equation
NON-SPINNING
OPERATING
RESERVE
NON_AGC
TOTAL
SPINNING
LOAD FOLLOW.
CONTROL
SPINNING
AGC
(Regulating)
REG Down
MW
GENERATION
Plant MAXMW  Plant MW   Re serves
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Joint Optimization
– Energy and A/S markets with price forecasts
– Optimal trade-off between energy and A/S
• Spin
• Non Spin
• Regulation Up
• Regulation Down
Energy
•Unused capacity can earn revenues with resulting unused
water still sold as energy at a later date
•Some of the unused capacity can be converted into energy
when reserve is called (Take)
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Physical Relations: Plants and Units
• Power-flow-head relationship (3-D)
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Spillway Equations
Q = Co · Le · Open · (hwl - E)Eo
E = Esill or twl
hwl
Free Overflow
hwl
ESill
Submerged
Flow
twl
ESill
Q = Cf · Le · (hwl - Esill)Ef
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Operational Constraints Representation
• Hydraulic Constraints
– Simple Constraints on Flow, storage (WL), MW
– Time aggregated constraints (linear)
• Max average
• Max/min between periods
– Relational constraints (including step functions)
• Electric Constraints
– Simple Max/ Min on generation
– Tieline flow (congestion)
– Reserve (min/max)
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27
Operational Constraints Representation
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Complexities in Formulation
• Uncertainty
– Inflow
– Load
– Market price
Long
Term
• Hydraulics
– Non-linear physical constraints
• generation with cross product (flow * head^a)
• Losses (quadratic)
• Spill representation
– Spatial/time connectivity
Short
Term
• Discreteness
– Start/stop costs
– Spinning reserve
– Non continuous operating range
Real
Time
• Large Scale
– Time dependent decisions (up to 200,000 decision variables / constraints)
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Preferred Schemes for Hydro
Linear Programming
•Piecewise linearization
•Successive Linearization
•Semi-heuristics
•
•
Decomposition
•Subproblems
•Bender’s cuts
•Dynamic Programming
•Nonlinear Programming
Plants are hydraulically and electrically connected
– Water conveyance
– Load, reserve
Fixed amount of water over time – strong temporal interdependency
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30
Long-term Planning
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Long Term Model Principles
31
• Consideration for Future Uncertainty
– Stochastic
• Detailed Physical Representation
• Simplified Time Definition
– Periods (week(s), month)
– Sub-period (peak, off-peak, weekend,…)
• Time Average answers
• Based on scenario analysis – consider all cross
correlations
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LT Vista Mathematical Model
Hydraulic network:
– arcs (plant, spill, river
reaches)
– nodes (reservoirs,
junctions)
Engine
Stochastic SLP (2 stage)
Detailed Plant Operation
Detailed constraint set
Benders Decomposition
•
Electric network:
-
Buses
tielines
Inputs:
- hydraulic: stochastic
inflow, start/end WL
- electric: transactions,
load
Constraints:
- hydraulic (flow,
elevation, etc.)
- electric (transmission,
etc.)
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LT Vista Methodology
33
• Two Stage LP
• Decomposition Master 1st Period / Future period
subproblem
Future 1
Future 2
NOW
Future 3
Future N
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LT Vista Methodology
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• Multi-dimensional Uncertainty -- Inflow, Market and
Load
Market
Hydrology
H1
H1_M1
H1_M2
H1_M3
H1_Mm
Load
H1_M2_L1_
H1_M2_L2
H1_M2_L3
H1_M2_Ll
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LT Vista Time Definition
• Period:
– basic model time step (e.g., 1 week)
• SubPeriod:
– Peak-off peak (Load duration) aggregation within periods
• Time blocks
– constraints tying several periods/subperiods
subperiods
period
Time block
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LT Vista Display – Probabilistic WL
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LT Vista Display – Probabilistic MW
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Short-term Scheduling
01/2012
Short Term Model Principles
•
•
•
•
39
Deterministic Model
Detailed Physical Representation
Detailed Hourly Time Definition
SLP numerical scheme with piecewise
representation:
– MW/Flow relation
– Tieline losses
• Unit Dispatch/Unit Commitment Subproblem
– Nonlinear Programming
– DP
• Spinning reserve allocation subproblem
• Integrated handshake with Long Term Model
• Market Analysis
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Unit Dispatch/ Unit Commitment Subproblem
•
•
•
•
Plant Representation based on optimal unit dispatch/ unit
commitment around base solution
Plant Generation function used in SLP
Best Dispatch answers used in scheduling
General LP problem formulation cannot deal with
discrete decisions – unit ON or unit OFF
Plant 1
Non continuous operation
Plant 2
Unit Dispatch
Model
•Snapshot Non
linear analysis
•Fixed Head
Plant N
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Spill Allocation
•
•
•
•
•
Aggregated spill representation
Piecewise linear representation
No flow zone
Sequencing issues – heuristic vs integer set
Stability issues
Spill 1
Spill 2
Spill N
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LT – ST Handshake
•
Type
– Economic
• Seasonal Reservoirs: Value of water in storage applied to end of opt period water
levels
• Other Reservoirs/head ponds: Max Target Water Levels at the end of opt period.
– Target Water Levels
• Seasonal Reservoirs: LT Target Levels applied to end of opt period water levels
• Other Reservoirs/head ponds: Max Target Water Levels at the end of opt period
– Target Flow Releases
• Seasonal Reservoirs: LT Target Levels applied to end of opt period water levels
• Other Reservoirs/head ponds: Max Target Water Levels at the end of opt period
•
Others
– meet target water levels defined by user
•
Custom
– Combination of above
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Spinning Reserve Allocation Subproblem
• Linearized formulation of spinning reserve
• Subproblem is to find best unit allocation to meet
spinning reserve requirements
• LP Unit representation
120
Reserve
100
80
Operating
Spin
Spin + Reg Down
60
40
20
0
0
20
40
60
80 100 120
MW Gen
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Reduction of Problem Size:
User Defined Time Grouping
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Total Bus Generation: Comparison
between Time Groupings
4 hr
2 hr
8 hr
01/2012
Reduction of Problem Size:
ON/OFF River Status
46
01/2012
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ST Vista Run Times (866 MHz)
Total Study Time
35.0
Time (minutes)
30.0
Cold Starts
25.0
Day
Ahead
Study
Period
20.0
15.0
10.0
Hot Starts
5.0
0.0
0
20000
40000
60000
80000
# of Constraints (row size)
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Semi-Heuristic Resolution Schemes
•
•
•
•
•
Plant retirement/commitment
Plant zone resolution
Uncontrolled spillway structure
Semi-heuristic – does not cover all solution space
Perturbation to the LP global problem
M
W
Flow
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Price-Volume Curves
Methodology
•
Cost sensitivity calculation
Future
MW
Base
Storage
Dev
$
Time
MWh
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Real Time Dispatch
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Real Time Model Principles
51
•
•
•
•
Deterministic Model
Detailed Physical Representation
Detailed sub hourly Time Definition
Detailed Unit Dispatch/Unit Commitment Subproblem
• Integrated handshake with Short Term Model
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Unit Commitment – Dispatch Rules
•
•
•
•
•
Minimum unit run time
Minimum unit down time
Maximum number of unit state changes in one time step
Unit start / stop costs
Dynamic unit status eligibility
•
•
•
•
Unit availability
Unit available for start
Unit available for shutdown
Unit fixed operations
• Chosen algorithm – Dynamic Programming optimization
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Unit Commitment – DP Formulation
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Unit Commitment – DP Features
• Only states derived from every time step, snap-shot, unit
dispatch results are considered
• Only eligible state paths are considered
• Two cost components are evaluated
• State transition costs ( unit start / stop costs )
• State operation costs ( cost of water to meet generation requirements )
• Objective function – minimize total dispatch cost
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Efficiency Gains
After
Before
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Conclusions
56
• Future Trends and Developments
– Quality of Short Term Schedule
• Robustness/stability
– Expansion of market analysis
– Handling of uncertainty in Short Term scheduling
– Higher flexibility/performance in LT stochastic analysis
01/2012